The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1  0 a^2*X a*X  0  1  1  1  1  1  1  1 a^2*X  0  1  1  X  1  1  X  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1  1  1  0  1  1 a*X  1 a^2*X  X a*X  X
 0  1  0  0  X a^2*X  1 a^2*X+a a^2  1  a a^2*X+1 a^2*X+1 a^2*X+a^2 a*X+a X+a  1 a^2 a^2*X+a^2  1  1  1  1 a*X  X a*X+1 X+a^2 a^2*X+a a*X+a  a  1  1 X+a^2 a^2*X+1 a*X a^2*X+a^2 a*X  1 a*X+1 a*X+1  1 a*X a*X+a^2 X+a X+a a^2*X  0 a*X+a  1 a*X+1 a^2*X+a^2  a X+1  1 a^2 X+a^2 a*X a^2*X a^2*X a*X a^2*X a^2*X
 0  0  1  1 a^2*X+a a^2 X+1 a^2*X+1 a*X+1 a^2  0  X  a a^2*X X+a a^2*X+a^2  1 a*X+a^2  a a*X+a^2 X+a X+1 a^2 a^2 a^2*X  X a^2*X+a^2 X+1 X+a a^2*X a*X+1 a^2*X  1  1  1 a*X a*X+1 X+1 a*X a^2*X+a^2 a*X+1  1 a^2*X+1 a*X+a^2 a*X+a^2  0 a*X+a^2 a^2*X+a^2 a^2*X+a a^2 a^2*X+a X+1 a*X  a  a  X  1 a*X+a  1  1  1  1
 0  0  0 a^2*X  0  0 a^2*X a^2*X a^2*X  X a*X  X  0 a*X  0  X  0  0 a^2*X  X a*X a*X a*X a^2*X  X  0 a^2*X  X a^2*X  0 a^2*X a^2*X  X a*X a^2*X  0  X  X a^2*X a*X  0 a*X a*X a^2*X  0 a^2*X  X a*X  0  0  X  0 a*X a^2*X a*X a*X a*X a*X  X  0 a*X a^2*X

generates a code of length 62 over F4[X]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+1848x^176+3276x^180+3720x^184+3012x^188+2283x^192+1476x^196+648x^200+108x^204+12x^208

The gray image is a linear code over GF(4) with n=248, k=7 and d=176.
This code was found by Heurico 1.16 in 96.4 seconds.